New Applications of Fast Lyapunov Indicator for Discrete-Time Dynamical Systems

In this work, the intention was to apply the Fast Lyapunov Indicator (FLI) for distinguishing between ordered and chaotic motion in some discrete-time dynamical systems. The behavior of certain discrete maps, like Gaussian maps, delayed logistic maps and 2-D, respectively 4-D symplectic maps studied by Froeschele has been studied and conclusions regarding FLI for ordered/chaotic orbits have been considered. The simplicity of the idea and the correlation between the conclusions obtained by FLI and other tools, like phase-plane or Lyapunov exponents, shows that FLI is a very consistent indicator in identifying ordered/chaotic orbits in discrete-time dynamical systems.